Tom Brady threw for three scores and ran for another in bringing the Patriots their fifth straight win. New England forced five New York turnovers.
New England improved to 8-3 while no other team in the AFC East has more than four victories. The Jets fell to 4-7.
The Patriots were already leading 14-0 with the second quarter nearing its midway point when New York quarterback Mark Sanchez collided with one of his own lineman while trying to avoid New England's pass rush.
The ball was knocked from Sanchez' grasp and Gregory quickly scooped it up on his way to a 32-yard touchdown.
On the ensuing kickoff Joe McKnight was hit by Devin McCourty and the ball popped into the air. Edelman grabbed it on the dead run and romped 22 yards for another score.
Edelman also caught a 46-yard touchdown pass from Bradey to finish off a 35-point New England second quarter. Brady's other scoring throws went for 3 yards to Wes Welker and 83 yards to Shane Vereen.
Bradey was 18-of-28 for 323 yards without an interception. The Patriots, who lead the NFL in total offense, barely missed reaching the 50-point mark for the second straight week. They ran over Indianapolis last weekend 59-24.
Sanchez completed 26-of-36 passes for 301 yards with one touchdown and one interception.
Senate Democrats to pull all-nighter on climate change
Interpol investigating stolen passports on missing flight